Let me start by writing the following about repentance and forgiveness with some appropriate scripture references.
1. Repentance is necessary for God to forgive us.
(Acts 2:38) Peter replied, "Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins.
(Acts 3:19) Repent, then, and turn to God, so that your sins may be wiped out, that times of refreshing may come from the Lord,
2. Forgiveness will not happen until these take place. If we do not repent we will perish
(Luke 13:1-5) Now there were some present at that time who told Jesus about the Galileans whose blood Pilate had mixed with their sacrifices. Jesus answered, "Do you think that these Galileans were worse sinners than all the other Galileans because they suffered this way? I tell you, no! But unless you repent, you too will all perish. Or those eighteen who died when the tower in Siloam fell on them do you think they were more guilty than all the others living in Jerusalem? I tell you, no! But unless you repent, you too will all perish."
3. And repentance isn't just for unbelievers. Repentance is an activity for believers which we continually practice as we fall into sin: "Those whom I love I rebuke and discipline. So be earnest and repent"
(Revelation 3:19) Those whom I love I rebuke and discipline. So be earnest, and repent. 20 Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with him, and he with me.
Luke 17:3-4 3 So watch yourselves. "If your brother sins, rebuke him, and if he repents, forgive him. If he sins against you seven times in a day, and seven times comes back to you and says, 'I repent,' forgive him.
2 Corinthians 7:9-10 yet now I am happy, not because you were made sorry, but because your sorrow led you to repentance. For you became sorrowful as God intended and so were not harmed in any way by us.
2 Peter 3:9 The Lord is not slow in keeping his promise, as some understand slowness. He is patient with you, not wanting anyone to perish, but everyone to come to repentance.
Revelation 2:5 Remember the height from which you have fallen! Repent and do the things you did at first. If you do not repent, I will come to you and remove your lampstand from its place.
Rev 3:3 Remember, therefore, what you have received and heard; obey it, and repent. But if you do not wake up, I will come like a thief, and you will not know at what time I will come to you.
4. Does this help with your questions about repentance or do you only want examples of forgiveness without repentance?
There are some isolated examples which I believe are acts of grace where there is not apparent repentance but my heart tells me that secretly, there was repentance involved here as well although it is not written. I am speaking about the story of what many call "The woman at the well." It is written in John 8:3-11:
3 And the scribes and the Pharisees bring a woman taken in adultery; and having set her in the midst,
4 they say unto him, Teacher, this woman hath been taken in adultery, in the very act.
5 Now in the law Moses commanded us to stone such: what then sayest thou of her?
6 And this they said, trying him, that they might have (whereof) to accuse him. But Jesus stooped down, and with his finger wrote on the ground.
7 But when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her.
8 And again he stooped down, and with his finger wrote on the ground.
9 And they, when they heard it, went out one by one, beginning from the eldest, (even) unto the last: and Jesus was left alone, and the woman, where she was, in the midst.
10 And Jesus lifted up himself, and said unto her, Woman, where are they? did no man condemn thee?
11 And she said, No man, Lord. And Jesus said, Neither do I condemn thee: go thy way; from henceforth sin no more .)
Another example is that of one of the criminals that was crucified beside Jesus who recognized Jesus was the son of God. One place it is written about is Luke 23:42-43:
"And he (the criminal) said, Jesus, remember me when thou comest in thy kingdom. And he Jesus) said unto him, Verily I say unto thee, today shalt thou be with me in Paradise."